An approximate controllability result with continuous spectrum : the Morse potential with dipolar interaction

Nabile Boussaid (1) , Marco Caponigro (2) , Thomas Chambrion (3, 4)

1 LMB - Laboratoire de Mathématiques de Besançon (UMR 6623)
2 M2N - Modélisation mathématique et numérique
3 SPHINX - Systems with physical heterogeneities : inverse problems, numerical simulation, control and stabilization
4 IECL - Institut Élie Cartan de Lorraine

This note presents a positive approximate controllability result for a bilinear quantum system modeling a chemical bond. The main difficulties are due to the presence of a continuous spectrum part for the uncontrolled Hamiltonian (modeled by a Morse potential) and the unboundedness of the interaction potential (dipolar interaction). The proof is based on averaging technique and spectral analysis.

Mots clés: averaging; quantum control; continuous spectrum; bilinear system

Domaines: Optimisation et contrôle [math.OC]

Nabile Boussaid, Marco Caponigro, Thomas Chambrion. An approximate controllability result with continuous spectrum : the Morse potential with dipolar interaction. SIAM Conference on Control and its applications, Jul 2015, Paris, France. ⟨hal-01143308⟩